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Andes Extremo is an excellent choice for paragliding and also offers other outdoor activities including rock climbing. You can book a tandem flight with a fantastic view on the Cochabamba valley for about Bs. 350. One of their rock climbing options is in Quarry Angostura, which will cost you US$45 per person for 1 day (half day) with a minimum of 2 people. The difficulty level is 5a-6c.
The statue is just a bit higher and larger than the one in Rio de Janeiro, making it the world's largest statue of Jesus until 2010, when a larger one was completed in Poland. It offers a great view of the city. Walk Calle Colombia until its eastern end, then a swift right: This park/playground is where the cable car goes from, Bs. 6.50 each way. You can also walk. The stairs are safe during the day. After sunset it is better to go in a group of 4 or more. However, the warning displayed at the cable car station, not to use the stairs, is obviously just there to make more money. The cable car is often under maintenance. There is no good way to know before heading out to the station, but the local newspaper is pretty good about updating any changes.
Display of native and non-native flora.
The main hospital in Cochabamba, Hospital Viedma, has a cute little medical museum attached, with some amazing old x-ray machines. The museum is near the corner of Venezuela and Oquendo.
Awesome archeological museum with mummies, deformed skulls, amazing pottery and other artifacts. Well worth a visit.
1760 convent that is restored for viewing.